Divers Tom Daley and Max Brick were part of England's Commonwealth Games team in Delhi that used Jerusalem as an anthem. Photograph: Cameron Spencer/Getty Images

David Cameron is apparently ready to back a campaign for England to have its own anthem for sports teams, and his personal choice would be Jerusalem, according to the British Future thinktank and the ConservativeHome website.

Since 2003 the England cricket team have routinely emerged from pavilions to Sir Hubert Parry's music set to William Blake's poem – except at Lord's, which does not play music through its sound system. English medal winners at the Commonwealth Games in Delhi in 2010 showed off their prizes proudly to Jerusalem after it replaced Land of Hope and Glory as the team's song – to the confusion of one competitor, the butterfly champion Fran Halsall, who started singing the old anthem on the podium before realising her mistake.

But the England rugby and football teams still stand chests puffed out to God Save the Queen. Last month the Lib Dem MP Greg Mulholland, who has regularly backed campaigns for England to have its own sporting anthem to rival Scotland's Flower of Scotland and Wales's Hen Wlad Fy Nhadau (Land of My Fathers), proposed that Euro 2012 should be the last international football tournament at which England compete without an English anthem, even if God Save the Queen remains the official one for UK teams.